In a time difference of arrival geolocation system the signal from a target emitter is received at three or more geographically distributed sensors. To determine a location of the emitter, it is necessary to calculate the difference in the arrival time of the same signal at each receiving sensor. These time differences (also referred to as the time difference of arrival or TDOA) correspond to differences in distance between the emitter and the receiving sensors since all signals travel at the speed of light. The distance between the target emitter and each sensor is given by d=ct, where c is the speed of light, t is the transmission time and d is the distance between the target emitter and the receiving sensor.
With the TDOA approach, a signal received at n receiving sites yields n(n−1)/2 pairs of time difference of arrival values from which the location of the emitter can be determined. Generally, the time difference of arrival of the same signal at any two receiving stations (referred to as a pairwise time difference of arrival) is a constant and yields a locus of points along a hyperbola. For example, possible locations of an emitter transmitting a signal arriving at a sensor S1 at t1 and arriving at a sensor S2 at t2 is defined by a locus of points comprising a hyperbolic curve, where the curve is defined by t2−t1=k1, where k1 is a constant.
With only two receiving stations using a TDOA method, it is generally not possible to determine a precise location for a target unit, but rather only a locus of points along a curve. Therefore, TDOA systems generally use at least three receiving stations to make a geolocation determination. For example, if the same signal is also received by a third sensor S3, two additional curves are computed based on the time difference of arrival of the signal at the three sensors taken in pairs. One such additional curve is determined by the time difference of arrival between sensors S1 and S3, and the other is determined by the time difference of arrival between sensors S2 and S3. The intersection of the three curves is the geolocation of the target emitter.
The target signal necessarily takes different paths to each sensor and may be corrupted by noise and interference as it propagates. Such noise and interference can reduce the accuracy of the target's determined location. The determination of the time difference of arrival of the signal at any two sensors is a problem in statistical estimation, with a time difference estimate (TDE) described by both a mean and a variance. The variance of the estimate determines the accuracy of the location solution and is affected by the signal bandwidth, signal-to-noise ratio and signal duration (the latter referred to as the coherent integration interval).
The present invention relates to determining a magnitude-squared coherence (MSC) of target signals and filtering the target signals based on the MSC to improve the accuracy of the TDE.